We report an ultrasonic sensor system based on a low-finesse Fabry-Perot interferometer (FPI) formed by two weak chirped fiber Bragg gratings (CFBGs) on a coiled single-mode fiber. The sensor system has several desirable features for practical applications in detecting ultrasound on a solid surface. By controlling the birefringence of the fiber coil during the sensor fabrication, the sensor is made insensitive to the polarization variations of the laser source. The circular symmetric structure of the fiber coil also renders the omnidirectional response of the sensor to ultrasound. While the fiber coil is bonded directly to the structure, the CFBGs are suspended from the structure and free from large background strains with little reduction to the sensitivity of the sensor. The low-finesse FPI features a sinusoidal reflection spectrum. Like the conventional phase-generated carried technique, a phase modulator is utilized to implement quadrature demodulation. Therefore, the sensing system is adaptive to large background perturbations experienced by the fiber coil.